Let \(G\)  be a finite group and \(S\)  be a generating set of \(G\) . Then, \(\text{Cay}(G, S)\)  denotes the Cayley graph [1]}, [2]}, [3]} of \(G\)  with the generating set \(S\) , where the set of vertices \(V\)  of \(\text{Cay}(G, S)\)  corresponds to the elements of \(G\) , and the set of edges \(E\)  of \(\text{Cay}(G, S)\)  corresponds to the action of generators in such a way that \(E=\lbrace <x, y>_g: x, y \in G \text{ and } g \in S \text{ such that } y=x\cdot g\rbrace \) . In this paper we assume that \(G\)  is a finite permutation group and the elements of \(S\)  are transpositions in \(\text{Cay}(G, S)\) . It follows that \(S\)  is closed under inverses, and \(E\)  is undirected. In other words, an edge \(<x, y>\)  of the resulting \(\text{Cay}(G, S)\)  is viewed as both \(<x, y>_g\)  and \(<y, x>_g\) .
If \(G\)  is a finite group and \(S\)  is a set of transpositions that generates \(G\) , then a transposition graph \(T = (<n>, S)\)  [3]} is an undirected graph in which \(<n>\)  denotes a vertex set of cardinality \(n\)  and each edge \(<i,\,j>\)  denotes transposition \((i\,j)\) . If a transposition graph is a tree, we call the resulting transposition graph as a transposition tree. We next provide examples of the generating sets for permutation groups including their transposition trees.
